Additional formal logic concepts and common informal logical fallacies with a short example of each, set II.
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- What is De Morgan's first law?
- The negation of a conjunction is the disjunction of the negations: not(A and B) = (not A) or (not B).
- What is De Morgan's second law?
- The negation of a disjunction is the conjunction of the negations: not(A or B) = (not A) and (not B).
- What is the contrapositive of a conditional, and is it logically equivalent to the original?
- The contrapositive of 'if A then B' is 'if not B then not A'. A conditional and its contrapositive are logically equivalent.
- What is a biconditional statement?
- A statement 'A if and only if B' that is true when A and B have the same truth value, both true or both false.
- What is a vacuous truth?
- A conditional 'if A then B' is vacuously true when the antecedent A is false, regardless of whether B is true or false.
- What is a tautology?
- A proposition that is true under all possible truth value assignments to its variables.
- What is a contradiction?
- A proposition that is false under all possible truth value assignments to its variables.
- What is a contingent proposition?
- A proposition that is true under some truth assignments and false under others, neither a tautology nor a contradiction.
- What is the fallacy of affirming the consequent?
- Arguing from 'if A then B' and 'B is true' to conclude 'therefore A is true', which does not follow logically.
- What is the fallacy of denying the antecedent?
- Arguing from 'if A then B' and 'A is false' to conclude 'therefore B is false', which does not follow logically.
- What is a disjunctive syllogism?
- A valid argument form: from 'A or B' and 'not A', you can validly conclude 'B'.
- What is a hypothetical syllogism?
- A valid argument form: from 'if A then B' and 'if B then C', you can validly conclude 'if A then C'.
- What is a material conditional?
- A conditional 'if A then B' that is false only when A is true and B is false; true in all other cases.
- What is an ad hominem fallacy?
- Attacking the person making an argument rather than addressing the argument itself, as if a character flaw refutes the claim.
- Give an example of an ad hominem fallacy.
- 'You cannot argue for gun control because you are a politician' instead of examining their actual reasons.